Bridging Physics and Deep Learning: An Autoencoder-Based Approach for Non-Invasive Estimation of Prostate Tissue Composition

Physics model-based approaches using Magnetic Resonance Imaging (MRI) have been developed to provide a non-invasive tool to estimate tissue composition by fitting the notoriously ill-conditioned sum-of-decaying-exponentials functions. However, even modest levels of noise can negatively impact the accuracy of such models. This study introduces a new paradigm that integrates the strengths of physics model-based and deep learning-based methods, while overcoming their respective weaknesses. We reformulated the MRI-based tissue composition estimation using a physics-informed autoencoder (PIA), transforming the problem from a least-squares fit into a robust deep learning framework. The PIA model consists of a trainable multi-head neural network encoder and a fixed, physics-informed decoder. Without a need for further fine-tuning for each new patient, the encoder's latent activations are utilized to derive prostate tissue composition estimates, such as volume fractions for each compartment along with their diffusivity and T2. PIA's estimates of tissue parameters are juxtaposed with the least-squares solution through both Monte Carlo simulations and the quantitative histology of in- vivo prostate scans. In-vivo evaluations, performed on 19 pathology-proven prostate cancer patients, have been validated with quantitative histology-based true tissue compositions. Both Monte Carlo and in-vivo evaluations reveal that PIA significantly outperforms the conventional least-squares solution on Pearson correlation and mean absolute error metrics. Notably, PIA was able to predict the diffusivity and T2 of each tissue compartment more accurately, whereas the least-squares method tends to pin these values to the extremities.